That is a nice work. I intend to use an optically tracked sphere for satellite. For 10 cm diameter it does not have enough orbits left, on Sputnik 1 orbit.

I searched and found Vanguard 1 had 16.5 cm diameter and 1.47 kg. As it orbits from 660 to 3840km its estimated lifetime is about 240 years. Could you run a simulation for 16.5 diameter sphere of 20 grams ? I would like to know the number of orbits for some altitude between Sputnik 1 and Vanguard 1.

Just for reference, I would like to know how well does it estimate Sputnik 1 lifetime. We know it performed 1440 orbits, and I think an estimate from 1000 to 2000 orbits would be a good precision result.

Unfortunately Sputnik doesn't seem to want to decay as fast as it should. It took 5124 orbits to come down. However, since this is a static atmospheric model and density can vary by large amounts in the thermosphere, I decided to see by what factor the density would need to increase to bring the simulation back into line with history. If I increase it by a factor of 3.54, then it lasts 1447 orbits.

Running the simulation on the n-prize satellite with the increased atmospheric density brings the lifetime from 165 orbits down to just 47.

In the future the code will have a much better dynamic atmospheric model which should produce better results without the need for a fudge factor, but for now this is the best I can do.

If you're shooting for optical tracking, you may have issues with a sphere that small. Sputnik itself was a larger and highly polished metal sphere, but was only barely visible with the naked eye. Apparently when most people looked for it, they more often than not saw the much larger rocket stage that put it there.

If you can get anything into space with a perigee of at least 500 km, it will stay there for a reasonable time, but that's a tall order without either a very steep (hence inefficient) launch trajectory, or some kind of attitude control and an engine re-light or dedicated apogee kick motor. Much easier is to aim for 250 - 300 km or so and give it all the delta-v you can.

One potential trick that might extend orbital lifetime is launching at night, that way your perigee will be over the night side and apogee over the day side. Solar radiation pressure will then act to reduce your apogee, but increase your perigee. Essentially it'd be trying to squash you into a more circular orbit, and since raising the perigee is the best way to extend orbital lifetime, especially of such a low density object, it could be useful.

The software I have CAN include that in the simulation, but I'll try that some other time.

The information you provided is really useful.I'll try to figure out whether I can afford a large enough sphere to be visible to the naked eye or not. Maybe I'll reach a decision only after complete data for fuel and guidance system is available.

This is off topic but I was thinking more about the apogee kick motor idea.

I had a thought that perhaps if you could spin up the last stage of your rocket such that it would maintain it's attitude during the burn, pointing more or less prograde, then half an orbit later it'll be pointing retrograde. If you had a kick motor mounted on the top of the payload it could fire "backwards" after some timer has counted down. It could be a dumb hobby rocket motor since you'd only need a small amount of delta-v to raise the perigee.

If you were in a 200 x 660 km orbit, and you were to do a prograde burn at apogee of 217 m/s, you'd then be in a 660 x 1000 km orbit. With a nice high orbit like that, you could likely get away with a much larger sphere and still have a very long orbital life time.